Dome Team = Offensive Team

Ok? You act like they’ve had decades of success. Even if they are successful, how long will that last once they lose their OC?

Really your whole point is moving the goal posts. There is no argument that refutes the Saints play on field turf and a temperature controlled stadium. What does that help the most besides kicking? Passing. Who’s best suited to build a passing oriented offense? A former QB who is adept at passing concepts. It’s a simple concept. Build your team starting with your natural advantages.
No, I'm giving you a clear example of opposite evidence, that you happen not to like.

The goal posts are all in their original position. Fast turf assists multiple parts of the game. It doesn't evidentially in isolation make a team 'better' in one particular phase, as much as you want it to.

Furthermore, even if it did, you still have to play 47-52% of your regular season games away in a location where this 'natural advantage' has zero bearing. Guess what wins in less than ideal field conditions more often than not? I'll give you a hint, it's not a large reliance on the passing game....